CN112975938A - Zero-space-based mechanical arm speed layer trajectory planning method - Google Patents

Zero-space-based mechanical arm speed layer trajectory planning method Download PDF

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CN112975938A
CN112975938A CN201911274963.XA CN201911274963A CN112975938A CN 112975938 A CN112975938 A CN 112975938A CN 201911274963 A CN201911274963 A CN 201911274963A CN 112975938 A CN112975938 A CN 112975938A
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mechanical arm
obstacle
task
obstacle avoidance
direction vector
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CN112975938B (en
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姜勇
王洪光
侯赵磊
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Shenyang Institute of Automation of CAS
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Shenyang Institute of Automation of CAS
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B25J9/1666—Avoiding collision or forbidden zones

Abstract

The invention relates to a zero-space-based collaborative mechanical arm speed layer trajectory planning method. An attraction speed function and a repulsion speed function are designed, so that several problems of a potential field method in a special scene are avoided; judging the movement trend of the barrier according to the moving direction and the included angle of the mechanical arm and the barrier, and realizing dynamic barrier avoidance track planning by superposing an additional direction vector on the basis of the original barrier avoidance direction; the tail end operation task and the obstacle avoidance task are subjected to priority processing by utilizing the characteristic of a null space of the mechanical arm, and the mechanical arm can complete the low-priority task under the condition of meeting the requirement of the high-priority task by mapping the low-priority task to the null space of the high-priority task. The invention can simultaneously complete the operation task at the tail end of the mechanical arm and the obstacle avoidance task of the body under the condition that the mechanical arm and the environment are safe under the dynamic unstructured environment based on the zero space characteristic of the mechanical arm.

Description

Zero-space-based mechanical arm speed layer trajectory planning method
Technical Field
The invention relates to the technical field of intelligent robots, in particular to a velocity layer trajectory planning method of a mechanical arm in a dynamic unstructured environment.
Background
The cooperative robot has the characteristics of man-machine fusion, safety, easiness in use, sensitivity, accuracy, flexibility, universality and the like, is suitable for the flexible manufacturing requirements of small batches, multiple varieties and user customization in the industrial field, has potential application prospects in the fields of service, medical treatment, electric power and the like, and becomes an important direction for leading the development of the next generation of industrial robots. In a dynamic unstructured task environment, how to dynamically adjust a motion track in real time according to environmental changes to realize autonomous obstacle avoidance and reach a target position is a key problem to be solved in collaborative robot application research.
When the mechanical arm senses an obstacle in the working space and the obstacle may interfere with the operation task of the mechanical arm, the mechanical arm should adjust its motion trajectory in time, so as to avoid collision. The mechanical arm can be regarded as a kinematic chain formed by connecting a series of connecting rods in series, so that the obstacle avoidance strategy of the body connecting rod needs to be considered in addition to the obstacle avoidance of the end effector in the process of trajectory planning.
Disclosure of Invention
The invention aims to provide a null-space-based mechanical arm speed layer trajectory planning method.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a null-space-based mechanical arm speed layer trajectory planning method comprises the following steps:
1) judging whether the mechanical arm reaches a target point or not according to the coordinate of the mechanical arm end effector, if so, ending the task, otherwise, performing the step 2);
2) judging whether the mechanical arm enters the range of the obstacle or not according to the closest distance between the mechanical arm and the obstacle, and entering the step 3) if the mechanical arm enters the range of the obstacle, or entering the step 7);
3) judging the movement trend of the barrier according to an included angle formed by the unit direction vector of the mechanical arm movement and the unit direction vector of the barrier movement, if the barrier approaches the mechanical arm, performing step 4), and if the barrier is far away from the mechanical arm, entering step 5);
4) solving the repulsion velocity vector of the mechanical arm, correcting the obstacle avoidance direction of the mechanical arm, and entering the step 6);
5) solving the repulsion velocity vector of the mechanical arm, and entering the step 6);
6) calculating an attraction speed vector and the control quantity of each joint of the mechanical arm according to a priority strategy, and entering step 9);
7) solving the attraction velocity vector of the mechanical arm, and entering the step 8);
8) calculating the control quantity of each joint of the mechanical arm, and entering the step 9);
9) and (5) controlling the mechanical arm to move by the upper computer according to the control quantity of each joint of the mechanical arm, and entering the step 1).
The step 3) is as follows:
the unit direction vector of the mechanical arm movement is
Figure BDA0002315318740000021
The unit direction vector from the closest point of the obstacle to the mechanical arm is
Figure BDA0002315318740000022
The unit direction vector of the movement of the obstacle is
Figure BDA0002315318740000023
When in use
Figure BDA0002315318740000024
In the process, the barrier moves towards the direction far away from the mechanical arm without adjusting the obstacle avoidance direction, and at the moment, the obstacle is moved towards the direction far away from the mechanical arm
Figure BDA0002315318740000025
When in use
Figure BDA0002315318740000026
At this time, the obstacle moves in a direction approaching the robot arm.
The repulsion velocity expression is:
Figure BDA0002315318740000027
wherein the content of the first and second substances,
Figure BDA0002315318740000028
in order to reject the velocity vector(s),
Figure BDA0002315318740000029
for the obstacle-avoiding direction of the arm, d0The size of the closest distance between the mechanical arm body and the barrier, dmGamma is a function parameter set by a human being and is the radius of the action range of the obstacle.
The obstacle avoidance direction of the correction mechanical arm is an extra direction vector superposed on the basis of the original obstacle avoidance direction, and the method specifically comprises the following steps:
the unit direction vector of the mechanical arm movement is
Figure BDA00023153187400000210
The unit direction vector from the closest point of the obstacle to the mechanical arm is
Figure BDA00023153187400000211
The unit direction vector of the movement of the obstacle is
Figure BDA00023153187400000212
The adjusted obstacle avoidance direction vector is as
Figure BDA00023153187400000213
On the basis of which the direction vector is superimposed
Figure BDA00023153187400000214
Wherein
Figure BDA00023153187400000215
Figure BDA00023153187400000216
Is oriented perpendicular to
Figure BDA00023153187400000217
And
Figure BDA00023153187400000218
the direction vector of the plane formed, i.e.
Figure BDA00023153187400000219
Figure BDA00023153187400000220
Is oriented perpendicular to
Figure BDA00023153187400000221
And
Figure BDA00023153187400000222
the direction vector of the plane formed, and
Figure BDA00023153187400000223
is less than 90 deg..
The priority policy is: the obstacle avoidance task of the mechanical arm is set to be high priority, the operation task of the mechanical arm end effector, namely the action task of the mechanical arm, is set to be low priority, and the expression that the operation task of the mechanical arm end effector and the obstacle avoidance task of the mechanical arm body are met simultaneously is as follows:
Figure BDA0002315318740000031
wherein the content of the first and second substances,
Figure BDA0002315318740000032
the control quantity required by the obstacle avoidance task of the mechanical arm,
Figure BDA0002315318740000033
the control quantity after the movement coupling caused by the obstacle avoidance task is subtracted from the low-priority task, namely the target task,
Figure BDA0002315318740000034
the rank of (d) corresponds to the size of the zero-space degree of freedom corresponding to the obstacle avoidance task,
Figure BDA0002315318740000035
the rank of (c) then corresponds to the size of the degree of freedom required by the end target task,
Figure BDA0002315318740000036
the control quantity of each joint of the mechanical arm,
Figure BDA0002315318740000037
is the pseudo-inverse of the Jacobian matrix at the obstacle avoidance point,
Figure BDA0002315318740000038
to reject velocity vectors, I is the identity matrix, J0Jacobian matrix at the point of obstacle avoidance, JeIs the Jacobian matrix corresponding to the job task,
Figure BDA0002315318740000039
to attract velocity vectors, αhThe smoothing factor is a value which depends on the minimum distance between the mechanical arm and the obstacle, and the expression is as follows:
Figure BDA00023153187400000310
wherein gamma and beta are adjustable parameters, and x is the minimum distance between the mechanical arm and the obstacle.
The expression of the suction speed is:
Figure BDA00023153187400000311
wherein the content of the first and second substances,
Figure BDA00023153187400000312
to attract velocity vectors, daIs composed of
Figure BDA00023153187400000313
Increases to a constant threshold, d is the distance of the end of the arm from the target point.
The invention has the following beneficial effects and advantages:
1. the invention can simultaneously meet the obstacle avoidance of the tail end of the mechanical arm and the body connecting rod, and ensure that the mechanical arm completes the operation task under the condition of ensuring the self and environmental safety.
2. The invention improves the reactive trajectory planning algorithm under the local environment, and can effectively deal with the complexity and unpredictability of the dynamic barrier in the motion process.
3. The operation speed is high. According to the invention, the control quantity is superposed on the velocity layer, so that the problems of parameter acquisition, complex calculation and the like caused by a mechanical arm dynamics model in the calculation process are solved.
Drawings
FIG. 1 is a flow chart of a method embodying the present invention;
FIG. 2 is a schematic diagram of an obstacle avoidance direction according to the present invention;
fig. 3 is a schematic diagram of the obstacle avoidance of the robot arm.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The invention relates to the technical field of intelligent robots, in particular to a velocity layer trajectory planning method of a mechanical arm in a dynamic unstructured environment. In this example, as shown in fig. 1, the following steps are included:
1) judging whether the mechanical arm reaches a target point or not according to the coordinate of the mechanical arm end effector, if so, ending the task, otherwise, performing the step 2);
2) judging whether the mechanical arm enters the range of the obstacle or not according to the closest distance between the mechanical arm and the obstacle, and entering the step 3) if the mechanical arm enters the range of the obstacle, or entering the step 7);
3) judging the movement trend of the barrier according to an included angle formed by the unit direction vector of the mechanical arm movement and the unit direction vector of the barrier movement, if the barrier approaches the mechanical arm, performing step 4), and if the barrier is far away from the mechanical arm, entering step 5);
4) solving the repulsion velocity vector of the mechanical arm, correcting the obstacle avoidance direction of the mechanical arm, and entering the step 6);
5) solving the repulsion velocity vector of the mechanical arm, and entering the step 6);
6) calculating an attraction speed vector and the control quantity of each joint of the mechanical arm according to a priority strategy, and entering step 9);
7) solving the attraction velocity vector of the mechanical arm, and entering the step 8);
8) calculating the control quantity of each joint of the mechanical arm, and entering the step 9);
9) and (5) controlling the mechanical arm to move by the upper computer according to the control quantity of each joint of the mechanical arm, and entering the step 1).
Considering the problem that the mechanical arm is farther from the target point, which may cause a large attraction speed, an attraction speed function is designed, and an expression thereof is as follows. By adopting the idea of a saturation function, the size of the suction speed gradually tends to be constant along with the increase of the distance between the tail end of the mechanical arm and the target point. Unlike a general saturation function, the suction velocity expression is modified at the inflection point of the function, so that the velocity of the mechanical arm at the inflection point is smoother.
Figure BDA0002315318740000051
Considering the problem that the existence of obstacles at the target point can cause the target point to be unreachable, a repulsive velocity function is designed, wherein dmIs the size of the range of action of the obstacle. As the distance between the mechanical arm body and the obstacle is reduced, the repelling speed of the mechanical arm tends to be stable. Therefore, when an obstacle exists near the target point, the repelling speed of the obstacle does not rapidly increase along with the shortening of the distance, and the action of a repelling speed field is slowed down. When the distance between the tail end of the mechanical arm and the target point is smaller than the distance between the tail end of the mechanical arm and the obstacle, the mechanical arm can tend to reach the target point by reducing the magnitude of the repulsion speed or removing the repulsion action and other strategies. Along with the distance between the mechanical arm body and the obstacle is increased, the repelling speed gradually tends to zero.
Figure BDA0002315318740000052
As shown in fig. 2, the dynamic trajectory planning method is implemented by superimposing an additional direction vector on the basis of the original obstacle avoidance direction:
assume that the unit direction vector of the robot arm movement is
Figure BDA0002315318740000053
The unit direction vector from the closest point of the barrier to the mechanical arm body is
Figure BDA0002315318740000054
The unit direction vector of the movement of the obstacle is
Figure BDA0002315318740000055
When in use
Figure BDA0002315318740000056
In the process, the barrier moves towards the direction far away from the mechanical arm, so that the barrier avoiding direction does not need to be adjusted, and at the moment, the barrier avoiding direction is adjusted
Figure BDA0002315318740000057
When in use
Figure BDA0002315318740000058
At this time, the obstacle moves in a direction approaching the robot arm. If the obstacle avoidance direction of the mechanical arm is not adjusted, if the moving speed of the obstacle is greater than that of the mechanical arm, collision may occur. The adjusted obstacle avoidance direction vector is as
Figure BDA0002315318740000059
On the basis of which the direction vector is superimposed
Figure BDA00023153187400000510
Wherein
Figure BDA00023153187400000511
Figure BDA00023153187400000512
In a direction perpendicular to
Figure BDA00023153187400000513
And
Figure BDA00023153187400000514
formed of planes, i.e.
Figure BDA00023153187400000515
Figure BDA00023153187400000516
In a direction perpendicular to
Figure BDA00023153187400000517
And
Figure BDA00023153187400000518
plane formed and with
Figure BDA00023153187400000519
Is less than 90 deg..
Fig. 3 shows a schematic diagram of obstacle avoidance of the mechanical arm on an obstacle. Wherein d ismIs the range of action of the obstacle, v0The repelling speed of the obstacle to the mechanical arm body is obtained,
Figure BDA00023153187400000520
the amount of velocity corresponding to the desired trajectory for the end effector. Meanwhile, the expressions of the operation task of the mechanical arm end effector and the obstacle avoidance task of the mechanical arm body are met, and the following steps are shown.
Figure BDA0002315318740000061
Wherein the content of the first and second substances,
Figure BDA0002315318740000062
the control quantity of each joint of the mechanical arm,
Figure BDA0002315318740000063
is the pseudo-inverse of the Jacobian matrix at the obstacle avoidance point,
Figure BDA0002315318740000064
to reject velocity vectors, I is the identity matrix, J0Jacobian matrix at the point of obstacle avoidance, JeIs the Jacobian matrix corresponding to the job task,
Figure BDA0002315318740000065
is an attraction velocity vector.
Figure BDA0002315318740000066
Wherein gamma and beta are adjustable parameters, and x is the minimum distance between the mechanical arm and the obstacle.

Claims (6)

1. A null space-based mechanical arm speed layer trajectory planning method is characterized by comprising the following steps:
1) judging whether the mechanical arm reaches a target point or not according to the coordinate of the mechanical arm end effector, if so, ending the task, otherwise, performing the step 2);
2) judging whether the mechanical arm enters the range of the obstacle or not according to the closest distance between the mechanical arm and the obstacle, and entering the step 3) if the mechanical arm enters the range of the obstacle, or entering the step 7);
3) judging the movement trend of the barrier according to an included angle formed by the unit direction vector of the mechanical arm movement and the unit direction vector of the barrier movement, if the barrier approaches the mechanical arm, performing step 4), and if the barrier is far away from the mechanical arm, entering step 5);
4) solving the repulsion velocity vector of the mechanical arm, correcting the obstacle avoidance direction of the mechanical arm, and entering the step 6);
5) solving the repulsion velocity vector of the mechanical arm, and entering the step 6);
6) calculating an attraction speed vector and the control quantity of each joint of the mechanical arm according to a priority strategy, and entering step 9);
7) solving the attraction velocity vector of the mechanical arm, and entering the step 8);
8) calculating the control quantity of each joint of the mechanical arm, and entering the step 9);
9) and (5) controlling the mechanical arm to move by the upper computer according to the control quantity of each joint of the mechanical arm, and entering the step 1).
2. The null-space-based mechanical arm speed layer trajectory planning method according to claim 1, wherein the step 3) is as follows:
the unit direction vector of the mechanical arm movement is
Figure FDA0002315318730000011
The unit direction vector from the closest point of the obstacle to the mechanical arm is
Figure FDA0002315318730000012
The unit direction vector of the movement of the obstacle is
Figure FDA0002315318730000013
When in use
Figure FDA0002315318730000014
In the process, the barrier moves towards the direction far away from the mechanical arm without adjusting the obstacle avoidance direction, and at the moment, the obstacle is moved towards the direction far away from the mechanical arm
Figure FDA0002315318730000015
When in use
Figure FDA0002315318730000016
At this time, the obstacle moves in a direction approaching the robot arm.
3. The null-space-based mechanical arm speed layer trajectory planning method according to claim 1, wherein the repulsion speed expression is as follows:
Figure FDA0002315318730000017
wherein the content of the first and second substances,
Figure FDA0002315318730000021
in order to reject the velocity vector(s),
Figure FDA0002315318730000022
for the obstacle-avoiding direction of the arm, d0The size of the closest distance between the mechanical arm body and the barrier, dmGamma is a function parameter set by a human being and is the radius of the action range of the obstacle.
4. The null-space-based mechanical arm velocity layer trajectory planning method according to claim 1, wherein the step of correcting the obstacle avoidance direction of the mechanical arm is to superimpose an additional direction vector on the basis of the original obstacle avoidance direction, and specifically comprises the steps of:
the unit direction vector of the mechanical arm movement is
Figure FDA0002315318730000023
The unit direction vector from the closest point of the obstacle to the mechanical arm is
Figure FDA0002315318730000024
The unit direction vector of the movement of the obstacle is
Figure FDA0002315318730000025
The adjusted obstacle avoidance direction vector is as
Figure FDA0002315318730000026
On the basis of which the direction vector is superimposed
Figure FDA0002315318730000027
Wherein
Figure FDA0002315318730000028
Figure FDA0002315318730000029
Is oriented perpendicular to
Figure FDA00023153187300000210
And
Figure FDA00023153187300000211
the direction vector of the plane formed, i.e.
Figure FDA00023153187300000212
Figure FDA00023153187300000213
Is oriented perpendicular to
Figure FDA00023153187300000214
And
Figure FDA00023153187300000215
the direction vector of the plane formed, and
Figure FDA00023153187300000216
is less than 90 deg..
5. The null-space-based mechanical arm speed layer trajectory planning method according to claim 1, wherein the priority policy is: the obstacle avoidance task of the mechanical arm is set to be high priority, the operation task of the mechanical arm end effector, namely the action task of the mechanical arm, is set to be low priority, and the expression that the operation task of the mechanical arm end effector and the obstacle avoidance task of the mechanical arm body are met simultaneously is as follows:
Figure FDA00023153187300000217
wherein the content of the first and second substances,
Figure FDA00023153187300000218
the control quantity required by the obstacle avoidance task of the mechanical arm,
Figure FDA00023153187300000219
the control quantity after the movement coupling caused by the obstacle avoidance task is subtracted from the low-priority task, namely the target task,
Figure FDA00023153187300000220
the rank of (d) corresponds to the size of the zero-space degree of freedom corresponding to the obstacle avoidance task,
Figure FDA00023153187300000221
the rank of (c) then corresponds to the size of the degree of freedom required by the end target task,
Figure FDA00023153187300000222
the control quantity of each joint of the mechanical arm,
Figure FDA00023153187300000223
is the pseudo-inverse of the Jacobian matrix at the obstacle avoidance point,
Figure FDA00023153187300000224
to reject velocity vectors, I is the identity matrix, J0Jacobian matrix at the point of obstacle avoidance, JeIs the Jacobian matrix corresponding to the job task,
Figure FDA00023153187300000225
to attract velocity vectors, αhThe smoothing factor is a value which depends on the minimum distance between the mechanical arm and the obstacle, and the expression is as follows:
Figure FDA00023153187300000226
wherein gamma and beta are adjustable parameters,xis the minimum distance between the robot arm and the obstacle.
6. The null-space-based manipulator velocity layer trajectory planning method according to claim 1, wherein the attraction velocity expression is as follows:
Figure FDA0002315318730000031
wherein the content of the first and second substances,
Figure FDA0002315318730000032
to attract velocity vectors, daIs composed of
Figure FDA0002315318730000033
Increases to a constant threshold, d is the distance of the end of the arm from the target point.
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